Second-order differential equations

Section 1 introduces some basic principles and terminology. Sections 2 and 3 give methods for finding the general solutions to one broad class of differential equations, that is, linear constant-coefficient second-order differential equations. Section 2 covers homogeneous equations and Section 3 covers inhomogeneous equations. Section 4 explains how extra information can be used to help to select particular solutions that are appropriate in given situations. Section 5 looks at the phenomenon of resonance to gain insights into the solutions of inhomogeneous linear constant-coefficient second-order differential equations.

Course learning outcomes

After studying this course, you should be able to:

• Understand the key role of the principle of superposition in the solution of linear constant-coefficient second-order differential equations
• Obtain the general solution of a homogeneous linear constant-coefficient second-order differential equation using the solutions of its auxiliary equation
• Use the method of undetermined coefficients to find a particular integral for an inhomogeneous linear constant-coefficient second-order differential equation with certain simple forms of right-hand-side function
• Obtain the general solution of an inhomogeneous linear constant-coefficient second-order differential equation by combining its complementary function with a particular integral
• Use the general solution together with a pair of initial or boundary conditions to obtain, when possible, a particular solution of a linear constant-coefficient second-order differential equation.